I went to Prague in late July 2010 for the Midsummer Combinatorics Workshop (an invitation-only event) and for Jan Hubička's PhD defence. Here is the diary.
I left home just before 9: much too early, but I didn't quite trust on-line check-in, and in any case it hadn't been been able to tell me which terminal the plane would leave from. The District Line train was absurdly crowded, with rush-hour compression early on Sunday morning.
At Barons Court, a Piccadilly Line train was arriving as we pulled in. It was going to Heathrow terminals 4 and 1,2,3. I took it, hoping that there would be a poster in the train telling me which terminal to go to, but there was only a poster telling me where to send a text message on my mobile. I jumped off at Hatton Cross and found a poster telling me that it was Terminal 4 I wanted. Fortunately the train waited long enough for me to jump back on, since the next Terminal 4 train was more than ten minutes away.
At the airport, the KLM bag drop was remarkably short, so I asked the man whether my bag would go as hand luggage; he assured me that it would. So I went through security and arrived in the departure longue half an hour before the gate was due to open; time to make a start on the write-up. The American senior citizens who went through security before me were congratulating one another on setting off the alarm; one said it was her replacement hip that had done it.
We boarded and were underway quite expeditiously. The scheduled journey time was 80 minutes; we were in the air for only half that time, though I was only off the plane a couple of minutes before scheduled arrival. We took off over Windsor Castle, with a view of a train crossing the river and the big wheel disfiguring the bank. Before I could spot any other landmarks we were in the clouds. Over Essex they parted enough to give views of Stansted Airport and a lot of fields of ripe grain.
I finished off a Sudoku, wrote the start of a talk, and watched some very interesting ice crystals on the outside of the window.
Then we were below the clouds, over the sea, and soon crossed the long straight sandy Dutch coast. The fields behind the sand dunes were much greener than in England, and indeed water was much in evidence, including on the runway when we landed. A group of passengers broke into applause. I had thought this was a Canadian habit; maybe they were Canadian. We were in the furthest corner of the huge airfield; the terminals and control tower looked like a distant city as we landed, and taxi-ing in we crossed a bridge under which went a river with footpaths on both sides.
Disembarkation was terribly slow, as people tried to manoeuvre huge cases out of the overhead racks. (I was a fool to worry; my bag was a tiddler by comparison.)
In the airport, it turned out that to get from terminal D to terminal C, even though it was in the same building, we had to go through Dutch immigration, security, and customs. I thought the USA was the only country to do this -- though, to be fair to the Dutch, they were more efficient and friendly than the Americans (though enormously thorough). The immigration officer didn't like my smudgy picture, even though he could see the original on his screen; the security man asked me three times whether I had a laptop, and didn't accept my answer, since it turned out he was actually asking whether it was in the black bag and got impatient with me for fiddling round with the shoulder bag to get it out; then, despite having to put passport, boarding pass, belt, even comb, through the scanner, I still set off the alarm and was subjected to a very thorough body search.
In-flight food on the plane had been a biscuit, and I decided I needed some lunch. I got caught up in a huge mob of people waving vouchers, and when I finally got through, the cashier was displeased with me for not haing 95 eurocents to give her the right change! What has happened to the Netherlands?
Anyway, I got a very nice sandwich, ate it, then went to the gate, where of course I was terribly early. I found a power point, and charged up the white toy while typing up the events so far. The V key on the white toy is starting to play up, sad to say. I also discovered that the white toy does not recognise the camera when connected to the USB port, so I have to take the card out and put it in.
The gate had been changed from C14 to C16, and later changed again to C11. So I packed up and went to the new gate, where I read my book for a while before boarding. Getting on the plane, I picked up the English-language Prague Post, which contained a rather disturbing report that the agency responsible for State-owned forests is planning to open them to logging.
Again we boarded and set off promptly. By the time I had read the paper and half the in-flight magazine, we were coming in to land in Prague.
Getting off was remarkably quick. I was near the front, and wasn't caught behind anyone with too much luggage; I walked straight through the baggage hall and customs, wondering why I hadn't seen any immigration desks, when I came out into the real world.
What a difference from my first visit to Prague, when I had to get a visa (no easy task then), and they nearly didn't let me out because the hotel hadn't registered me with the police!
Anyway, there was a kiosk which sold me a transport ticket for 26 crowns (one-sixth the price of the airport bus, to say nothing of taxis). The next number 119 bus was due in five minutes, and came right on time; it took me to Dejvická metro (on the way we saw an accident on the freeway roundabout, with police and ambulance attending), where the train took me quickly to Staroměstská, and a short walk brought me to the door of the Karolinum.
It was locked, but I remembered there was an entrance at the back, so I wandered round. It was locked too. So back to the front, and I pressed the buzzer. I was expecting someone to speak, but instead someone came to open the door. I recognised her (and she me) from my last visit. She showed me my room and brought me an ethernet cable and a username and password.
I tried the computer; it didn't work. But I noticed it also said Wi-Fi, so I tried that, and it worked fine. I just checked a few things, and went out after food. My keys don't let me back in at night; the instructions are to press the red button!
I walked down to the Charles Bridge. There was a very nice light behind the bridge statues and the castle, but the crowds were appalling. In addition to the street artists and buskers, quite a bit of the bridge was closed off for repair.
I fought my way over the bridge, bought a sandwich in the small supermarket, and went into the park on Kampa Island to eat it. By the "big chair" near the entrance to the lock was a row of yellow penguins (which I had first, on seeing them from a distance, taken to be something connected with the navigation). After that I walked down to the next bridge and crossed over. Several structures at the ends of the bridge were under repair, and had rather unexpected images on the coverings.
I noticed that the word for "estate agency", which is "realty" in the USA, is, inappropriately, "reality" here.
I turned in through the maze of streets, following my nose, but got quite disastrously lost; so badly, in fact, that I passed the same restaurant twice! When I saw the Old Theatre, I knew where I was; I had seen it from the other side while looking for a way into the Karolinum, with a big pantechnicon parked outside (it was still there). So I was soon back. The walk did get me a few pictures.
I expected to have some trouble sleeping. There was a lot of music going on outside, beginning with a lugubrious violin, but with ever-increasing levels of synth pop. Also, it was quite hot, though the old building is not windproof and pleasant draughts circulated. In fact, I went straight to sleep, and saw nothing until the morning light came.
I have a vast room; I could hold a formal dance in my sitting room, complete with a small orchestra. Separate bedroom, bathroom, and toilet, and an anteroom where the clothes cupboard is.
There was only one person at breakfast when I arrived. He was a psychologist from Tucson, Arizona, who had been at a conference in Brno, but had been recommended to spend a day in Prague before leaving, and someone had booked a room in the Karolinum for him. He was quite overweight, but was determined to see the Golden Mile, even though he was falling asleep in his chair. (He was diabetic and was short of his articifial sweetener; he couldn't face coffee without it but was very reluctant to use sugar.)
I left my room just after 9; the back door was open and the receptionist refused to let me out the front way. But it took me quite a while to find the way out through the maze (eventually I went through the door marked "Rectorat", which worked). As a result, I was very slightly late; Jarik had already started making the announcements before the meeting started.
There were four talks before lunch. They were by Paweł Prałat, firefighting on graphs; Geoff Whittle, matroid representations; Dhruv Mubayi, counting structures in hypergraphs; and Dragan Masulović, on the complexity of hom-hom (for graphs with loops at each vertex, it is co-NP compete).
Geoff's was a nice talk, ranging from why the title of Peter Vamos' paper "The missing axiom of matroid theory is lost forever" is misleading and has skewed research for thirty years to why properties of real-representable matroids should be counted among Kant's "synthetic a priori" statements (he says, try visualising hyperbolic space in which the lines are seen as "straight" – I responded, think of the Beltrami model).
Dragan mentioned, in passing, a homomorphism version of the Engeler–Ryll-Nardzewski–Svenonius theorem. I wonder whether he has already solved Sam's question?
We had been given lunch tickets which included a beer. After lunch, there was no formal programme; Mike Newman took Geoff and me to a well-hidden coffee shop he knew, and we had a leisurely coffee, before heading back to our hotels, and agreeing to meet at 6:30 for dinner.
I discovered that I didn't have the date of Honza's defence; I thought it was Thursday but something he said made me think it might be tomorrow. I looked through all my files but couldn't find it. I suspect it is on paper and I left it in my office. So I did some preparation, just in case.
Geoff and I arrived at the meeting point on time. After 15 minutes, when Mike had still not come, we agreed to have a beer, and if he hadn't arried when we'd finished, to go off and find a place ourselves. He came just after we'd ordered and before the beer came, so we had a beer there and then set off. Mike knew an Italian restaurant outside the touristy part of town, so we went there. (Prague is not a good city for vegetarians; this probably explains his knowledge of good eating places.) We had a good meal, then walked home, and parted by our hotel. Geoff and Mike had both had substantial time shifts and were wilting a little.
Back home I worked for a while writing my extended abstract, then wrote up my diary before bedtime.
The man from Tucson was there at breakfast. He had had a good day, though the tour bus had broken down and they had to send for another. He does want to come back again.
After breakfast I found my way with rather less difficulty out of the Karolinum, and walked over to Malastrana, stopping on the way at the Bio-Market for toothpaste and shampoo.
The morning's talks were by Reza Naserasr, on homomorphisms from planar graphs to projective cubes (by which he means what I call folded cubes); Jan Foniok, on unique-sink orientations of hypercubes (they hope to find a better polynomial-time algorithm for linear programming, one which is polynomial in the numbers of variables and constraints, if arithmetic operations have a time cost of one, unlike present algorithms which are polynomial in the entire input size); Jiri Fiala, on contracting claw-free graphs to the path of length 4; and Miklós Ruszinkó, on partitioning edge-coloured complete graphs into monochromatic cycles.
Reza had a question aimed specifically at me, on highly symmetric induced subgraphs of folded cubes. For the folded 7-cube, his favoured subgraphs are the Kneser graph and the Coxeter graph (the subgraph of the Kneser graph obtained by deleting a Fano plane); I suggested that in the folded 11-cube, after the Kneser graph, he should delete a S(4,5,11), to get a nice 2-arc transitive graph on 396 points with valency 5.
I also learned something from Foniok's talk, namely the existence of a paper by Fukuda et al. about the flip graph of acyclic orientations of a given graph, which may be of some use to Celia and me.
At coffee time, Andrew Goodall suggested that I come on a little trip to the town of Tábor, about 80km south of Prague, where Honza Hubička comes from; it was the first day of an exhibition of old photographs of the town by his forebears, who had a photographic business there about the turn of the century. Not knowing quite what this would entail, I accepted.
After the last talk, Mike grabbed me to tell me something about a discovery of his on the question of the clique and chromatic numbers of the square of the Hamming graph. He says that is related to the Bailey–Cameron–Connelly paper on Sudoku. On thinking about it later, I realised that he has rediscovered some facts about perfect 1-error-correcting codes, with entirely different and possibly new proofs, and of course this has relevance to the synchronization project; the existence of a linear perfect code (for any number e of errors) implies that the core of the 2e-th power of the Hamming graph is complete. Sad to say, the non-sychronizing ranks which are obtained this way are not new.
We went to lunch, after which I waited for the Tábor party (who had gone out to lunch) in the square in front of the department. The beautifully clear and sunny morning was past, and there were big white clouds in the sky. We took the tram and metro to the railway station, where we bought a group ticket for five and went and got on the train, with a quarter of an hour to spare. We were in a compartment in a corridor carriage, an experience not available in Britain any more. Unfortunately, because of engineering work, we had to disembark and catch a bus at a certain point.
While waiting for the bus to leave, I read a plaque on the wall of the station. In Czech and English, it told of a luxurious royal waiting room there, still partly preserved. It seems that Kaiser Wilhelm and Archduke Franz Ferdinand met there, five weeks before the latter's assassination; it is believed that they discussed preparations for war.
The bus took us down the highway, first through rolling fields not totally unlike the Darling Downs, then through a hillier, more forested region. It stopped at one station on the way. Just before the station where we were to board another train, down came the rain, really heavily. The bus pulled up and we had to run through the rain, scrambling over wet rails and ballast and up the steps into the train. The first compartment we tried was flooded; the window had been left open. The second, however, was fine. Another fifteen minutes brought us to Tábor.
We walked through a pleasant long narrow park flanked by nineteenth-century buildings, and came to narrower streets of the older part of the town. Spots of rain began, and soon it was tipping down with great ferocity. We sheltered under a balcony, supported by carved stone arms, over the doorway of a shoe shop, for some time until the rain stopped. Just a little further up was a coffee shop, and we decided to go there when the rain eased up a bit. While we were there, the rain stopped and the sun came out; but as soon as we finished and paid, down it came again, so we had another long wait in the doorway.
Finally it was light enough that we could continue. Through the old town square, down a narrow street past a deep excavation, and out into another small square. On a corner was a building which was a chapel (seventh-day adventist, I think) with a gallery beneath; this is where the exhibition was.
I thought that the first day of an exhibition meant just that, but there was an event going on with a substantial crowd of people: speeches and music in the chapel, Honza, his parents, sister, and various kith and kin. The photos, many of them showing things that no longer existed, and some showing buildings before and after restoration, had been taken by Honza's great-great-grandfather and great-grandfather. (His grandparents had also been photographers, but moved more in the direction of art photography.) The restoration was by a famous architect who was wedded to the gothic, and many lovely old buildings had been gothicised; he had also worked in other places such as Prague Castle, but had not been given such free rein there. There were also several showing ordinary life back then: tanners, the cattle market, the cabbage market, a farm boy. After the speeches, Honza gave me a guided tour of the exhibition.
They have a huge collection of old plates of various types. (There had been many more; the Communists nationalised the business and made Honza's grandparents employees. The archive was their private property, so they sent the grandfather to prison for a couple of years so they could get their hands on it. A lot of material, thought to be threatening to the regime because it illustrated that things were not worse in the past, was simply destroyed.) At present they are doing a lot of work, both to conserve the original plates, and to digitise as much as possible in high resolution. Everything is being made public on the website, which is well worth a look.
Then there was another talk, illustrated by projections of some of the pictures. We didn't stay for that; Honza gave us a guided tour of the town, to see many of the buildings in the pictures, and also walk through a lovely beech wood on the side of a hill overlooking a stream, with a very interesting fungus.
We ended up at Honza's parents' house, where a large group of people fed on traditional soup made from wild mushrooms. The house was full of an astonishing collection of things: paintings of trees in bright colours, musical instruments on the walls, a piano identical to the one Dvořák used, etc. Honza gave me a book of his grandmother's photographs and a short history of the studio.
Finally we caught a bus to the station, Honza with us. Fortunately we didn't have to decant onto buses; the train took us all the way (it was now quite late), but didn't go very fast. It was 10:45 when we arried back in Prague. It was less than ten minutes walk to the Karolinum, where I went straight to bed.
Up in time to bath before breakfast. Geoff was there so I put my two ideas of yesterday to him. He liked the idea of transforming Escher's "Circle Limit" pictures to the Beltrami model. On the subject of matroid representability being independent of the type of geometry (elliptic, Euclidean or hyperbolic), he more or less said, that is the point; this escapes from the usual controversy about whether Euclidean, rather than non-Euclidean, geometry is innate, and asks more general questions. He said that his physicist colleague tells him that there has been essentially no work on this in the physics community.
I was a minute or two late getting to Malastrana, but arrived before anything had started. I was down as fourth speaker; the first three were Mike Newman, who talked about a logic for matroids (which allows quantification over subsets of the set of elements but forbids alternation of quantifiers), allowing him to prove that in this logic the real-representable matroids are not finitely axiomatisable; Petr Kolman on duality for multicommodity and multiroute flows; and Stefan Kreutzer on drawing graphs in 3-space in a manner which is linkless or (stronger) flat, where a flat embedding is one in which every graph circuit bounds a disc meeting the graph only in the circuit. He showed (if I have it right) that this is not really stronger.
At coffee time Jarik took me off to give me some "pocket money" for my stay in Prague. I am not short of crowns now!
My talk went well, writing on the blackboard rather than risking technology. (Mike Newman had had his netbook let him down, to the slight detriment of his talk.)
After lunch we walked up the hill for the conference excursion, a guided tour of parts of Strahov monastery which ordinary tourists don't get to see. The main library room was closed for repair, but a smaller library had a lot of interesting stuff, including a ceiling painting of the creation which is claimed to show the heliocentric system despite being painted when it was contrary to Catholic dogma.
We also saw the gallery. One thing that it made very clear is that paintings from the late fourteenth century, far from being inferior to Renaissance paintings made with knowledge of perspective, were actually much better. The clarity in these old pictures was quite extraordinary.
After the tour, I joined Martin Klazar, Geoff, Mike, and a Hungarian whose name I didn't catch, and wandered down to the Hrocha for a couple of beers. Mike, who finished first, was given a third beer, but the waitress was good enough to take it away again.
Then up for the conference dinner: chicken and salad, a skewer of meat and peppers with potatoes, and a large piece of cake; Becherovka, more beer, and coffee. After a while I wandered back home. Still some work to do on Honza's thesis!
This morning, as well as having a last-minute read through Honza's thesis, I put all the photos so far onto a stick. On previous trips to Prague, I have taken some really good photos; this time I haven't reached the same level.
There were five talks: first Hebert Pérez-Rosés, on voltage-graph constructions for large graphs with given diameter and girth (including some group-theoretic trivia which will give this stuff a bad name); Martin Kupec and Jan Volec, on different aspects of fractional colourings; a characteristically fine talk by Jiri Matousek, showing how the answer to a simple question about Seidel switching classes (of graphs with n vertices and fixed edge density which happen to have fewest edges in their switching class, which one minimises the number of triples in the corresponding two-graph, and what is this minimum?) would plug into a result of Gromov and give a better lower bound for the maximum number of simplexes covering a point, in the collection of all simplexes spanned by n given points; and Michel Pocchiola, on generalised pseudotriangulations (this seemed to be bell-ringing sequences which reverse the order of the bells, but he's interested in points where two bells decide not to change places).
Something in what he said suggested to me that perhaps there is a known result about the determinant of the matrix whose antidiagonals carry Catalan numbers, index decreasing by one at each step; experiment suggests it is always one. If I can prove it I will probably put it in the book as an exercise.
I learned that the defence is at 3pm, the first of three that afternoon (but I am not involved in the others, unlike one dreadful occasion in Rome). So I got dressed and sat around waiting until the time came.
The bureacracy was quite different from anywhere else. The defence is public, but the chair must establish that there is a quorum of the committee and that all the papers have been correctly assembled. Jarik gave a few words about Honza, then he gave his presentation. Due to some last-minute editing glitch, the word "ultrahomogeneous" came out everywhere as "ultraultrahomogeneous", which caused considerable mirth. Then I gave my comments, and Pultr gave his, both positive. The audience were sent out while the committee voted (on proper voting slips, in Czech); we were unanimously in favour of passing the candidate. So everyone trooped back in for the announcement. After that, Honza's sister and friends had organised refreshments; those who were on the next committee grabbed something and dashed back into the room, while the rest of us stood around for a while.
Honza invited me to his dinner party at a nearby restaurant at 7:30; I decided to go back to the hotel in between, and got directions before setting off. Crossing the Charles Bridge I saw three cellists playing the theme from "The Magnificent Seven". They must have been playing it for a while; I overtook two people whistling the theme. As I came through the Old Town Square, the clock was just about to chime, and the place was absolutely packed, except right in front of the clock; so I walked there.
Back in my room, I lay down for a few minutes, and went instantly to sleep, waking up just in time to get to the restaurant at the appointed time. Most people were already there, and two tables were full; but there was a free seat at the end of the smaller table. (Later, two more people came, and we moved to a larger table, keeping roughly the same layout.) I had a splended meal: smoked halibut, then a traditional Czech concoction of smoked duck stuffed with paté and served with red cabbage and potatoes.
I was sitting next to Honza's sister Eva and her boyfriend. We had a very good conversation: she is an architect, and we spent some time comparing mathematics, music and architecture, as well as comparing our experiences as students, and wondering which of mathematics, software engineering, or running the photographic museum will actually become Honza's primary career.
After dinner, we went to a wine bar for a farewell drink, but found it closed. Someone suggested another: it turned out to be the same place Mike had taken Geoff and me earlier in the week for coffee. Downstairs were a few tables, right next to the cellar where the wine was kept, so the experts could just step into the cellar with the waitress to choose a few bottles.
Jarik revealed that there will be a showing of the film they made about Endre Szemerédi's honorary degree tomorrow.
I had a good talk with Honza Kratochvíl. He had chaired Honza Hubička's defence, and had had a student of his own also defending his thesis succesfully. We talked about music, and he told me that his favourite band was ELP; I said I'd never seen them play but had seen the Nice back in the late 60s. We strolled home over the next bridge along, much more peaceful than the Charles bridge, with light reflecting in the water, and through the relatively quiet streets of the New Town to Můstek, where he took the metro and I went back to the Karolinum.
On the way to Malastrana for the last day of the conference, I was struck by the notice on the cars drawn up in the square. In broken English, they seemed to suggest that you could buy a car for 1200 crowns, and for an extra 300 they would throw in the castle!
There were two talks: Pavel Klavík on extending partial interval representations of graphs; and Maia Stein, a nice talk on extending results on finite graphs, where average degree bounds force certain kinds of subgraph, topological minor, or minor, to infinite graph, where average degree is hard to define. This reminded me of my old conjecture on defining the average edge-density of arbitrary infinite graphs; so when the next thing on the programme turned out to be the problem session, I proposed it, and got more interest than it usually drums up. Maybe someone will solve it.
After coffee, Roman Nedela talked about regular and Archimedean maps, after which we had a showing of the film about the honorary degree awarded to Endre Szemerédi last month. It was a well-produced film, though inevitably the soundtrack is a mixture of Czech, Hungarian, English and Latin (and mathematics), with no subtitles. Some of the shots of Endre and Jarik in their robes had a real old master feel to them.
After lunch, the next thing was Jarik's guided tour of the modern art collection, which was to start at 3. This gave me time for a quick walk up the hill to the castle. They were changing the guard at the north gate; after that I went out and walked round the garden. The greenhouse was open for a small entry fee, so I went in and looked: lovely orchids and other dramatic flowering plants. Then I walked round the gardens, back through the castle, and down the hill a different way.Following my comments yesterday, it struck me that I do take pictures differently now. Before, I composed the picture in the camera as carefully as I could; now I am quite happy if I get the object of interest in the shot at full optical zoom, and trust that I will be able to crop it later. Good or bad thing?
Then we were off to the National Gallery. I have been round it on one of Jarik's tours before, but it is always good to have another look. One thing struck me. We spent a lot of time on the Kupkas, from his abstract period. Just before his first abstract, almost the last of his symbolist works was a woman in a red and blue dress. It struck me that if you removed her head and feet and just looked at her torso in the dress, it was very similar to his first red-and-blue abstract.
His series of small sketches, ideas which later recurred in his more substantial abstract works, was also extremely impressive.
Afterwards, Jarik declared that he was going for a beer. Geoff Whittle, Dhruv Mubayi and I went with him, and had a very good discussion about many things including the future of mathematical publication (a very serious topic) and, indeed, the future health of mathematics.
Then Jarik caught the tram home, while the other three of us walked down town. Dhruv went to catch the metro, while Geoff and I found a fairly small place to eat and had a cheap but decent traditional Czech meal (duck for him, rabbit for me). Then home for an early night.
As arranged, I phoned Jarik when I was ready to set out, to arrange a time to meet. (The place was already agreed.) Then I set out. It was an absolutely glorious day, the light supremely clear in the Old Town Square as I walked to the metro station.
I had planned to buy enough tickets for the rest of my stay, but the man in the ticket office did a beautiful mime of having no change, so I dug in my purse and managed to find enough small coins for one single, which I bought. The train came fairly soon, and I was at the appointed meeting place exactly as Jarik drove up.
The purpose of his trip was to pick up a few pictures stored in his mother's apartment in the town of Rakovník, about an hour's drive west of Prague. (They are to be exhibited in Budapest, I think in conjunction with a conference there next week.) After a while, in the middle of a beautiful forest, the traffic slowed to a crawl – it turned out to be caused by two very large pieces of machinery ahead. We crawled the rest of the way to the town.
The first element in the town's name means "crayfish". Jarik told me the legend of its origin. It seems that, at a time of plague and famine, a woman decided to kill herself and her children, by eating the (supposedly poisonous) crayfish in the river. So she prepared a meal. The next morning, instead of waking up dead as she had expected, they all felt much stronger! The crayfish is commemorated in the town's coat of arms and on several buildings in the main square.
We went to the apartment, on the top floor of a slightly down-at-heel block (though most of the inhabitants had beautiful window boxes). The pictures were stored in one room, covered with plastic sheeting, as a workman had been installing new windows. We dug out the right box with a little difficulty, and Jarik chose five; he will whittle the choice down further at home.
Then, after a turn through the old town square, we set off for the village of Křivoklát, where there is an ancient royal castle on a hill dominating the village, and (more importantly) where he has a house. It is an extraordinary house, one of the first modernist houses anywhere in the world (built in 1928). The story is that a film producer had asked the modernist pioneer Le Courbusier to design a movie; one of his sketches was of a house, and the producer got the local builder to use the sketch as a design for his house in Křivoklát. It has a narrow outside staircase which was a Le Courbusier trademark (and now also an indoor staircase which Jarik has put in).
The setting was extraordinary, too. The house is right beside a small stream, the one which runs down from Rakovník; beyond the stream is a hiking trail, then a railway, then the hill rising very steeply several hundred metres. The garden has some lovely features: a small pool covered by a waterlily just coming into flower; an old and extremely bent apple tree; some silver cedars recently planted. However, it is all a bit overgrown; Jarik has little time to live there himself (though hopes to have more), and pays a man to cut the grass (but this doesn't seem to happen).
The modernist house was set among traditional rural life. Woodsmoke came from a chimney; one neighbour was washing cucumbers, while another was cutting up firewood.
The name "Křivoklát" means something like "crooked clearing", though nobody is quite sure why.
After some desultory weeding, and clearing an old bird's nest from the light on the first floor balcony, we walked down to one of the village pubs, the Hotel Sýkora; it was a bit early but the courtyard of the pub was very pleasant. We started with soup with liver dumplings. One of the specials was wild boar with cabbage; we both chose this, and it was probably the best meal I have had on this trip, and only a fraction of the cost of a meal in Prague (105 crowns for the main course). We had a plate of pancakes to share for dessert; just as well since I probably couldn't have managed one on my own.
We went back to the house for coffee. I said that I was definitely intending to come to the Czech republic sometime and do some hiking; Jarik immediately offered to rent the house to me cheaply. It is in the middle of a huge royal forest with lots of hiking trails. On leaving, we went to the tourist information, where I got a 1:50000 map of the area.
We drove down to see the big river into which the stream flows. Coming back there was a spectacular view of the castle. Then we drove back to Prague, first along a small road through the forest, and then to the village of Lány (the name apparently meaning "field" or "plain" and, according to Jarik, cognate with the Dutch "laan"), which had both the museum and burial place of the statesman Masaryk, and the birthplace of the mathematician Loewner.
Driving back to Prague, we had a couple of near misses. First, while worrying about what his wife would say if he unexpectedly turned up with me, he nearly turned off into the wrong lane at the roundabout (at almost exactly the place I'd seen an accident on the way in to Prague last Sunday). Then his mobile rang, and trying to extricate it from his pocket he ran the car up onto the kerb. It was someone phoning about the exhibition, so he told them to call back in half an hour.
He dropped me at the big roundabout in Dejvická, where I decided to get the metro back to Staromětská rather than walking. I now had a 100 crown note, which I thought would be OK. But there was no ticket office at Dejvická, and so I had to break the note by buying a bottle of water and then feed coins into a machine.
In the Old Town Square, there was a folk festival going on. (This is eastern European folk, people in embroidered dresses or jackets and funny hats doing traditional dancing rather than the British idea that it is the singing that counts). Numerous marching bands went along the street outside my hotel window.
Jan Saxl had asked me for an elegant proof that a primitive group containing a double transposition is symmetric or alternating. I thought about that for a while. (Why does a mathematician in the 21st century have to think about something which was resolved in the 19th? Because it's fun, of course!) When I got stuck, I went out for a walk through the back streets of New Town, huge houses with ornate frontages on either side of gritty empty streets.
At one point I met up with Mike Newman going the other way. He was off to see friends, but told me that he is sure his argument that arbitrary perfect codes give colourings of powers of the Hamming graph is correct. But he was not yet ready to explain it. He'll mail it to me when it is done.
I stopped in at a garden restaurant and had a meal, then continued my perambulation along the river to the Rudolfinum and back to the Old Town Square.
Outside the hotel, a group of four musicians playing bagpipes, hurdy-gurdy, lute, and drum had just begun playing my favourite Radio Tarifa track. So I listened to them for a while before going in. I reckoned I could listen just as well from my room; but, almost as soon as I arrived, they stopped. So I packed my things and had an early night.
I was woken up a couple of times by Saturday night noise outside, once at midnight and once at 5am, but I slept pretty soundly and woke just in time for a bath before breakfast.
At breakfast, as well as Geoff, there was a Korean man who had been at the world symposium on Czech literature, in which he is a specialist. He was keen to talk, and asked our names, where we came from, and what we were doing in Prague. He spends a month here every year. After he went, Geoff and I talked about the influence of Czech on Latin American literature: Kafka on Marquez, Jan Neruda on Pablo Neruda.
I got ready to go and had a last browse through the Prague Post before consigning it to the bin. There was a story about a 2-billion-euro tunnel being dug under Prague; it has had several collapses and attracted many complaints from people under whom it is burrowing, but work continues in advance of the safety report.
Then I checked out and set off to walk to Dejvická: through the Old Town Square, over Charles Bridge, up the hill through Malastrana. At the Castle, they were changing the guard at the front gate, and there were hundreds of tourists milling around, so I had to wait until they'd finished before I could go in. Fortunately the tourists all stopped just inside, so I could be on my way unimpeded.
Out of the north gate and down the hill, I came to the tunnel works I had just been reading about. The fences were decorated by poster-size versions of children's pictures making out that lots of traffic is a good thing, but I could see the huge disruption and the potential for damage to fine old buildings and open spaces.
Despite my attempts to walk slowly, I was at Dejvická in less than an hour. I found that all the coffee shops were shut, and I had not enough change left for a coffee from a machine; so I went to the Freshland shop and had a smoothie to kill time and get change for a ticket.
The bus came in about ten minutes; the journey was uneventful apart from one occasion where the door alarm contined to sound after we were underway. At the airport, the first machine I tried was out of action, and before I found a second, a helpful girl was explaining to me that I had to type in my e-ticket number. (I checked in on-line but couldn't print the boarding pass, of course). Once again, despite removing my belt, I set off the alarm and got body-searched. But I was into the departure lounge, far too early, so I had a sandwich and killed time.
A fine example of international broken English:
PLEASE, CHECK THE SIZE OF YOUR HAND BAG IF IT DOESN'T FIT INTO THE FRAME, VIA CHECK-IN COUNTER.
Once boarding began, it was all fairly quick. I had the window seat in the front row, so they had to take my handbag away for takeoff and landing. There was very good visibility of forests and fields at first; I looked out for the places I had seen yesterday, without success. Then there was intermittent cloud, with some view of the earth beneath. Soon we came to a big cloudbank, after which there was little to see of the earth; so I finished off the double transpositions and wrote them up, and then watched the clouds until we were there.
We came down over the flat, damp Netherlands, with canals and windmills, and landed much closer to the terminal. So then another long wait for the next flight. The lens fell out of my glasses, but I had plenty of time to make repairs. When we finally moved there were three barriers: security check, passport and boarding card check (which I failed because I had not had to enter my passport number when I checked in but KLM needed it) and a final wait at the gate.
A delay in getting the baggage on board meant that we lost our place in the queue and were three-quarters of an hour late leaving the gate, a tedious wait. No view, and all casual reading matter consumed during the wait, so I just sat patiently.
And the trip wound to its dreary end. Stacked briefly over Heathrow, and parked on the tarmac for ten minutes, we reached the gate to find a malfunction which took them a little while to fix. So we were an hour late getting off the plane. Then immigration took an hour, the most horrifying queue I have ever seen anywhere in the world. I missed a train by a whisker, and the next one came in and sat for ages before setting off. Back in Britain all right.
I hate travelling...